Alysha has just won a lottery. She will receive a payment of $8,000 at the end...

Alysha has just won a lottery. She will receive a payment of $8,000 at the end of each year for 9 years. As an alternative, she can choose an immediate payment of $55,000.

A. Which alternative should she pick if the interest rate is 4 percent: make a payment at the end of each year or an immediate payment? (choose)

B. What would the interest rate have to be for Alysha to be indifferent about the two alternatives? (Round answer to 4 decimal places, e.g. 25.2341%. Do not round your intermediate calculations.)

Solutions

Expert Solution

Present value of annuity = Annuity * [1 - 1 / (1 + r)^n] / r

Present value of annuity = 8000 * [1 - 1 / (1 + 0.04)^9] / 0.04

Present value of annuity = 8000 * [1 - 0.702587] / 0.04

Present value of annuity = 8000 * 7.435332

Present value of annuity = $59,482.65

Present value of 1st option = $59,482.65

Present value of 2nd option = $50,000

It is better to choose the first option as it has the higher present value.

Interest rate infifferent will be the IRR

IRR = 5.7544%

jeff jeffy answered 2 years ago

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